1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
|
/* -*- Mode: Asm -*- */
/* Copyright (c) 2002 Michael Stumpf <mistumpf@de.pepperl-fuchs.com>
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in
the documentation and/or other materials provided with the
distribution.
* Neither the name of the copyright holders nor the names of
contributors may be used to endorse or promote products derived
from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
/* $Id: fp_cosinus.S,v 1.7.2.1 2005/12/11 19:40:01 aesok Exp $ */
/*
fp_cosinus.S is part of FPlib V 0.3.0 ported to avr-as
for details see readme.fplib
*----------------------------------------------------------------------------------------
*
* A = cosinus(A) with A = [0...2PI[
*
* _ _ _ _ _ _
* |\ / \ | / | / |\ ;
* |a\ b c / d a \ b | c /d | / | \ ;
* +--\-----/-------- => ---\--+--/--- => +--/--- => +--X--- ;
* 0 \ / 2pi -pi \ | / pi 0| / pi | / pi/2 ;
* \_/ \_/ _/ _/ ;
* cos(x-PI) = cos(x) = cos(x) ;
* -cos(x) cos(-x)
* section sign
* a b c d a b c d a b c d a b c d
* + - - + - + + - - + + - + + + +
* sign complement for sections b + c
*/
#if !defined(__DOXYGEN__)
#include "gasava.inc"
#include "macros.inc"
#include "fplib.inc"
TEXT_SEG(fplib, __fp_cosinus)
FUNCTION(__fp_cosinus)
GLOBAL(__fp_cosinus) ; input A = [-2PI...2PI[
PUSH rSI0
ANDI rA3,0x7F ; input A = [0...2PI[
LDI rB3,0xC0
LDI rB2,0x49
LDI rB1,0x0F
LDI rB0,0xDB ; load -PI
RCALL _U(__addsf3) ; now A = [-PI..+PI[
LDI rSI0,0x80 ; assume sign complement (b,c)
ANDI rA3,0x7F ; positive cos(x-PI) = cos(-(x-PI)) = -cos(x)
LDI rB3,0x3F
LDI rB2,0xC9
LDI rB1,0x0F
LDI rB0,0xDB ; load PI/2
CP rA0,rB0 ;
CPC rA1,rB1 ;
CPC rA2,rB2
CPC rA3,rB3 ; cmp A to PI/2
BRCS 1f ; branch if lower
; now (A = x) > PI/2, B = PI/2
LDI rB3,0xC0
LDI rB2,0x49 ; B = -PI
RCALL _U(__addsf3) ; PI-A = -(A+-PI)
CLR rSI0 ; no sign complement (a,d)
1:
RCALL _U(square) ; x
ORI rA3,0x80 ; -x
;
LDI ZL,LOW(table_cos) ;
LDI ZH,HIGH(table_cos) ;
RCALL _U(__fp_powerseries) ;
EOR rA3,rSI0 ; complement sign
POP rSI0
RET
ENDFUNC
PGM_SECTION
/* cos(x) = ( 1 - x(1/2! - x(1/4! - x(1/6! - x(1/8! - x(1/10! - x(1/12! - x(1/14!))
*/
table_cos:
DCB 8 ; no of table entries - 1 (preload value)
; looks like 6 steps are sufficient
; 7 steps for sin(pi) == 0
;;DCB 0x4A, 0x34, 0x13, 0xC3 ;, 0x1E ; 1/18!
DCB 0x29, 0x57, 0x3F, 0x9F ; 1/16!
DCB 0x2D, 0x49, 0xCB, 0xA5 ; 1/14!
DCB 0x31, 0x0F, 0x76, 0xC7 ; 1/12!
DCB 0x34, 0x93, 0xF2, 0x7E ; 1/10!
DCB 0x37, 0xD0, 0x0D, 0x01 ; 1/8!
DCB 0x3A, 0xB6, 0x0B, 0x61 ; 1/6!
DCB 0x3D, 0x2A, 0xAA, 0xAB ; 1/4! = 1/24
DCB 0x3F, 0x00, 0x00, 0x00 ; 1/2!
DCB 0x3F, 0x80, 0x00, 0x00 ; 1.0
DCB 0x00
#endif /* not __DOXYGEN__ */
|
